%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV515+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:59:25 PM UTC 2026
% Result : Theorem 0.21s 0.51s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 19
% Syntax : Number of formulae : 154 ( 16 unt; 14 def)
% Number of atoms : 632 ( 0 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 753 ( 275 ~; 367 |; 95 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 20 ( 19 usr; 15 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 152 ( 0 sgn 127 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X0] :
? [X1] :
( ( g_true_only(X1,X0)
& ( g_both(X1,X1)
| g_true_only(X1,X1) ) )
| ( g_both(X1,X0)
& ( g_false_only(X1,X1)
| g_true_only(X1,X1) ) )
| ( g_false_only(X1,X0)
& ( g_false_only(X1,X1)
| g_both(X1,X1) ) ) )
| ( ? [X0] :
( ? [X1] :
( g_both(X1,X0)
& g_both(X1,X1) )
& ~ ? [X1] :
( ( g_true_only(X1,X0)
& ( g_both(X1,X1)
| g_true_only(X1,X1) ) )
| ( g_both(X1,X0)
& ( g_false_only(X1,X1)
| g_true_only(X1,X1) ) )
| ( g_false_only(X1,X0)
& ( g_false_only(X1,X1)
| g_both(X1,X1) ) ) ) )
& ~ ? [X0] :
! [X1] :
( ( g_true_only(X1,X0)
& g_false_only(X1,X1) )
| ( g_false_only(X1,X0)
& g_true_only(X1,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nc1) ).
fof(f2,negated_conjecture,
~ ( ! [X0] :
? [X1] :
( ( g_true_only(X1,X0)
& ( g_both(X1,X1)
| g_true_only(X1,X1) ) )
| ( g_both(X1,X0)
& ( g_false_only(X1,X1)
| g_true_only(X1,X1) ) )
| ( g_false_only(X1,X0)
& ( g_false_only(X1,X1)
| g_both(X1,X1) ) ) )
| ( ? [X0] :
( ? [X1] :
( g_both(X1,X0)
& g_both(X1,X1) )
& ~ ? [X1] :
( ( g_true_only(X1,X0)
& ( g_both(X1,X1)
| g_true_only(X1,X1) ) )
| ( g_both(X1,X0)
& ( g_false_only(X1,X1)
| g_true_only(X1,X1) ) )
| ( g_false_only(X1,X0)
& ( g_false_only(X1,X1)
| g_both(X1,X1) ) ) ) )
& ~ ? [X0] :
! [X1] :
( ( g_true_only(X1,X0)
& g_false_only(X1,X1) )
| ( g_false_only(X1,X0)
& g_true_only(X1,X1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,axiom,
! [X0,X1] :
( g_true_only(X0,X1)
<=> ( g_true(X0,X1)
& ~ g_false(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',true_only_g) ).
fof(f4,axiom,
! [X0,X1] :
( g_both(X0,X1)
<=> ( g_true(X0,X1)
& g_false(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',both_g) ).
fof(f5,axiom,
! [X0,X1] :
( g_false_only(X0,X1)
<=> ( g_false(X0,X1)
& ~ g_true(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_only_g) ).
fof(f6,axiom,
! [X0,X1] :
( g_true_only(X0,X1)
| g_both(X0,X1)
| g_false_only(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exhaustion_g) ).
fof(f7,plain,
~ ( ! [X0] :
? [X1] :
( ( g_true_only(X1,X0)
& ( g_both(X1,X1)
| g_true_only(X1,X1) ) )
| ( g_both(X1,X0)
& ( g_false_only(X1,X1)
| g_true_only(X1,X1) ) )
| ( g_false_only(X1,X0)
& ( g_false_only(X1,X1)
| g_both(X1,X1) ) ) )
| ( ? [X2] :
( ? [X3] :
( g_both(X3,X2)
& g_both(X3,X3) )
& ~ ? [X4] :
( ( g_true_only(X4,X2)
& ( g_both(X4,X4)
| g_true_only(X4,X4) ) )
| ( g_both(X4,X2)
& ( g_false_only(X4,X4)
| g_true_only(X4,X4) ) )
| ( g_false_only(X4,X2)
& ( g_false_only(X4,X4)
| g_both(X4,X4) ) ) ) )
& ~ ? [X5] :
! [X6] :
( ( g_true_only(X6,X5)
& g_false_only(X6,X6) )
| ( g_false_only(X6,X5)
& g_true_only(X6,X6) ) ) ) ),
inference(rectify,[],[f2]) ).
fof(f8,plain,
( ? [X0] :
! [X1] :
( ( ~ g_true_only(X1,X0)
| ( ~ g_both(X1,X1)
& ~ g_true_only(X1,X1) ) )
& ( ~ g_both(X1,X0)
| ( ~ g_false_only(X1,X1)
& ~ g_true_only(X1,X1) ) )
& ( ~ g_false_only(X1,X0)
| ( ~ g_false_only(X1,X1)
& ~ g_both(X1,X1) ) ) )
& ( ! [X2] :
( ! [X3] :
( ~ g_both(X3,X2)
| ~ g_both(X3,X3) )
| ? [X4] :
( ( g_true_only(X4,X2)
& ( g_both(X4,X4)
| g_true_only(X4,X4) ) )
| ( g_both(X4,X2)
& ( g_false_only(X4,X4)
| g_true_only(X4,X4) ) )
| ( g_false_only(X4,X2)
& ( g_false_only(X4,X4)
| g_both(X4,X4) ) ) ) )
| ? [X5] :
! [X6] :
( ( g_true_only(X6,X5)
& g_false_only(X6,X6) )
| ( g_false_only(X6,X5)
& g_true_only(X6,X6) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f9,definition,
( ! [X2] :
( ! [X3] :
( ~ g_both(X3,X2)
| ~ g_both(X3,X3) )
| ? [X4] :
( ( g_true_only(X4,X2)
& ( g_both(X4,X4)
| g_true_only(X4,X4) ) )
| ( g_both(X4,X2)
& ( g_false_only(X4,X4)
| g_true_only(X4,X4) ) )
| ( g_false_only(X4,X2)
& ( g_false_only(X4,X4)
| g_both(X4,X4) ) ) ) )
| ~ sP0 ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f10,plain,
( ? [X0] :
! [X1] :
( ( ~ g_true_only(X1,X0)
| ( ~ g_both(X1,X1)
& ~ g_true_only(X1,X1) ) )
& ( ~ g_both(X1,X0)
| ( ~ g_false_only(X1,X1)
& ~ g_true_only(X1,X1) ) )
& ( ~ g_false_only(X1,X0)
| ( ~ g_false_only(X1,X1)
& ~ g_both(X1,X1) ) ) )
& ( sP0
| ? [X5] :
! [X6] :
( ( g_true_only(X6,X5)
& g_false_only(X6,X6) )
| ( g_false_only(X6,X5)
& g_true_only(X6,X6) ) ) ) ),
inference(definition_folding,[],[f8,f9]) ).
fof(f11,plain,
( ! [X2] :
( ! [X3] :
( ~ g_both(X3,X2)
| ~ g_both(X3,X3) )
| ? [X4] :
( ( g_true_only(X4,X2)
& ( g_both(X4,X4)
| g_true_only(X4,X4) ) )
| ( g_both(X4,X2)
& ( g_false_only(X4,X4)
| g_true_only(X4,X4) ) )
| ( g_false_only(X4,X2)
& ( g_false_only(X4,X4)
| g_both(X4,X4) ) ) ) )
| ~ sP0 ),
inference(nnf_transformation,[],[f9]) ).
fof(f12,plain,
( ! [X0] :
( ! [X1] :
( ~ g_both(X1,X0)
| ~ g_both(X1,X1) )
| ? [X2] :
( ( g_true_only(X2,X0)
& ( g_both(X2,X2)
| g_true_only(X2,X2) ) )
| ( g_both(X2,X0)
& ( g_false_only(X2,X2)
| g_true_only(X2,X2) ) )
| ( g_false_only(X2,X0)
& ( g_false_only(X2,X2)
| g_both(X2,X2) ) ) ) )
| ~ sP0 ),
inference(rectify,[],[f11]) ).
fof(f13,plain,
( ! [X0] :
( ! [X1] :
( ~ g_both(X1,X0)
| ~ g_both(X1,X1) )
| ( g_true_only(sK1(X0),X0)
& ( g_both(sK1(X0),sK1(X0))
| g_true_only(sK1(X0),sK1(X0)) ) )
| ( g_both(sK1(X0),X0)
& ( g_false_only(sK1(X0),sK1(X0))
| g_true_only(sK1(X0),sK1(X0)) ) )
| ( g_false_only(sK1(X0),X0)
& ( g_false_only(sK1(X0),sK1(X0))
| g_both(sK1(X0),sK1(X0)) ) ) )
| ~ sP0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0))],[f12]) ).
fof(f14,plain,
( ? [X0] :
! [X1] :
( ( ~ g_true_only(X1,X0)
| ( ~ g_both(X1,X1)
& ~ g_true_only(X1,X1) ) )
& ( ~ g_both(X1,X0)
| ( ~ g_false_only(X1,X1)
& ~ g_true_only(X1,X1) ) )
& ( ~ g_false_only(X1,X0)
| ( ~ g_false_only(X1,X1)
& ~ g_both(X1,X1) ) ) )
& ( sP0
| ? [X2] :
! [X3] :
( ( g_true_only(X3,X2)
& g_false_only(X3,X3) )
| ( g_false_only(X3,X2)
& g_true_only(X3,X3) ) ) ) ),
inference(rectify,[],[f10]) ).
fof(f15,plain,
( ! [X1] :
( ( ~ g_true_only(X1,sK2)
| ( ~ g_both(X1,X1)
& ~ g_true_only(X1,X1) ) )
& ( ~ g_both(X1,sK2)
| ( ~ g_false_only(X1,X1)
& ~ g_true_only(X1,X1) ) )
& ( ~ g_false_only(X1,sK2)
| ( ~ g_false_only(X1,X1)
& ~ g_both(X1,X1) ) ) )
& ( sP0
| ! [X3] :
( ( g_true_only(X3,sK3)
& g_false_only(X3,X3) )
| ( g_false_only(X3,sK3)
& g_true_only(X3,X3) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X2,sK3)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( ( g_true_only(X0,X1)
| ~ g_true(X0,X1)
| g_false(X0,X1) )
& ( ( g_true(X0,X1)
& ~ g_false(X0,X1) )
| ~ g_true_only(X0,X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f17,plain,
! [X0,X1] :
( ( g_true_only(X0,X1)
| ~ g_true(X0,X1)
| g_false(X0,X1) )
& ( ( g_true(X0,X1)
& ~ g_false(X0,X1) )
| ~ g_true_only(X0,X1) ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( g_both(X0,X1)
| ~ g_true(X0,X1)
| ~ g_false(X0,X1) )
& ( ( g_true(X0,X1)
& g_false(X0,X1) )
| ~ g_both(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f19,plain,
! [X0,X1] :
( ( g_both(X0,X1)
| ~ g_true(X0,X1)
| ~ g_false(X0,X1) )
& ( ( g_true(X0,X1)
& g_false(X0,X1) )
| ~ g_both(X0,X1) ) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( g_false_only(X0,X1)
| ~ g_false(X0,X1)
| g_true(X0,X1) )
& ( ( g_false(X0,X1)
& ~ g_true(X0,X1) )
| ~ g_false_only(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f21,plain,
! [X0,X1] :
( ( g_false_only(X0,X1)
| ~ g_false(X0,X1)
| g_true(X0,X1) )
& ( ( g_false(X0,X1)
& ~ g_true(X0,X1) )
| ~ g_false_only(X0,X1) ) ),
inference(flattening,[],[f20]) ).
fof(f25,plain,
! [X0,X1] :
( ~ g_both(X1,X0)
| ~ g_both(X1,X1)
| g_both(sK1(X0),sK1(X0))
| g_true_only(sK1(X0),sK1(X0))
| g_both(sK1(X0),X0)
| g_false_only(sK1(X0),X0)
| ~ sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f27,plain,
! [X0,X1] :
( ~ g_both(X1,X0)
| ~ g_both(X1,X1)
| g_true_only(sK1(X0),X0)
| g_false_only(sK1(X0),sK1(X0))
| g_true_only(sK1(X0),sK1(X0))
| g_false_only(sK1(X0),X0)
| ~ sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f28,plain,
! [X0,X1] :
( ~ g_both(X1,X0)
| ~ g_both(X1,X1)
| g_true_only(sK1(X0),X0)
| g_both(sK1(X0),X0)
| g_false_only(sK1(X0),sK1(X0))
| g_both(sK1(X0),sK1(X0))
| ~ sP0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f30,plain,
! [X3] :
( sP0
| g_false_only(X3,X3)
| g_true_only(X3,X3) ),
inference(cnf_transformation,[],[f15]) ).
fof(f34,plain,
! [X1] :
( ~ g_false_only(X1,sK2)
| ~ g_both(X1,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f35,plain,
! [X1] :
( ~ g_false_only(X1,sK2)
| ~ g_false_only(X1,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f36,plain,
! [X1] :
( ~ g_both(X1,sK2)
| ~ g_true_only(X1,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f37,plain,
! [X1] :
( ~ g_both(X1,sK2)
| ~ g_false_only(X1,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f38,plain,
! [X1] :
( ~ g_true_only(X1,sK2)
| ~ g_true_only(X1,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f39,plain,
! [X1] :
( ~ g_true_only(X1,sK2)
| ~ g_both(X1,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f40,plain,
! [X0,X1] :
( ~ g_false(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f43,plain,
! [X0,X1] :
( g_false(X0,X1)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
! [X0,X1] :
( g_true(X0,X1)
| ~ g_both(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f46,plain,
! [X0,X1] :
( ~ g_true(X0,X1)
| ~ g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f49,plain,
! [X0,X1] :
( g_true_only(X0,X1)
| g_both(X0,X1)
| g_false_only(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f51,plain,
! [X0,X1] :
( g_both(X1,X0)
| g_both(X1,X1)
| ~ g_true_only(sK1(X0),X0)
| ~ g_both(sK1(X0),X0)
| g_false_only(sK1(X0),sK1(X0))
| ~ g_both(sK1(X0),sK1(X0))
| ~ sP0 ),
inference(consistent_polarity_flipping,[],[f28]) ).
fof(f52,plain,
! [X0,X1] :
( g_both(X1,X0)
| g_both(X1,X1)
| ~ g_true_only(sK1(X0),X0)
| g_false_only(sK1(X0),sK1(X0))
| ~ g_true_only(sK1(X0),sK1(X0))
| g_false_only(sK1(X0),X0)
| ~ sP0 ),
inference(consistent_polarity_flipping,[],[f27]) ).
fof(f54,plain,
! [X0,X1] :
( g_both(X1,X0)
| g_both(X1,X1)
| ~ g_both(sK1(X0),sK1(X0))
| ~ g_true_only(sK1(X0),sK1(X0))
| ~ g_both(sK1(X0),X0)
| g_false_only(sK1(X0),X0)
| ~ sP0 ),
inference(consistent_polarity_flipping,[],[f25]) ).
fof(f58,plain,
! [X1] :
( g_true_only(X1,sK2)
| g_both(X1,X1) ),
inference(consistent_polarity_flipping,[],[f39]) ).
fof(f59,plain,
! [X1] :
( g_true_only(X1,sK2)
| g_true_only(X1,X1) ),
inference(consistent_polarity_flipping,[],[f38]) ).
fof(f60,plain,
! [X1] :
( g_both(X1,sK2)
| ~ g_false_only(X1,X1) ),
inference(consistent_polarity_flipping,[],[f37]) ).
fof(f61,plain,
! [X1] :
( g_both(X1,sK2)
| g_true_only(X1,X1) ),
inference(consistent_polarity_flipping,[],[f36]) ).
fof(f62,plain,
! [X1] :
( ~ g_false_only(X1,sK2)
| g_both(X1,X1) ),
inference(consistent_polarity_flipping,[],[f34]) ).
fof(f65,plain,
! [X3] :
( sP0
| g_false_only(X3,X3)
| ~ g_true_only(X3,X3) ),
inference(consistent_polarity_flipping,[],[f30]) ).
fof(f68,plain,
! [X0,X1] :
( g_false(X0,X1)
| g_true_only(X0,X1) ),
inference(consistent_polarity_flipping,[],[f40]) ).
fof(f70,plain,
! [X0,X1] :
( g_true(X0,X1)
| g_both(X0,X1) ),
inference(consistent_polarity_flipping,[],[f44]) ).
fof(f71,plain,
! [X0,X1] :
( ~ g_false(X0,X1)
| g_both(X0,X1) ),
inference(consistent_polarity_flipping,[],[f43]) ).
fof(f74,plain,
! [X0,X1] :
( g_false_only(X0,X1)
| ~ g_both(X0,X1)
| ~ g_true_only(X0,X1) ),
inference(consistent_polarity_flipping,[],[f49]) ).
fof(f80,definition,
( spl4_1
<=> ! [X3] :
( g_false_only(X3,X3)
| ~ g_true_only(X3,X3) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f81,plain,
( ! [X3] :
( g_false_only(X3,X3)
| ~ g_true_only(X3,X3) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f83,definition,
( spl4_2
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f86,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f65,f83,f80]) ).
fof(f100,definition,
( spl4_6
<=> ! [X0,X1] :
( g_both(X1,X0)
| g_false_only(sK1(X0),X0)
| ~ g_both(sK1(X0),X0)
| ~ g_true_only(sK1(X0),sK1(X0))
| ~ g_both(sK1(X0),sK1(X0))
| g_both(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
fof(f101,plain,
( ! [X0,X1] :
( g_false_only(sK1(X0),X0)
| g_both(X1,X0)
| ~ g_both(sK1(X0),X0)
| ~ g_true_only(sK1(X0),sK1(X0))
| ~ g_both(sK1(X0),sK1(X0))
| g_both(X1,X1) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f102,plain,
( ~ spl4_2
| spl4_6 ),
inference(avatar_split_clause,[],[f54,f100,f83]) ).
fof(f104,definition,
( spl4_7
<=> ! [X0,X1] :
( g_both(X1,X0)
| g_false_only(sK1(X0),X0)
| ~ g_true_only(sK1(X0),sK1(X0))
| g_false_only(sK1(X0),sK1(X0))
| ~ g_true_only(sK1(X0),X0)
| g_both(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
fof(f105,plain,
( ! [X0,X1] :
( g_false_only(sK1(X0),sK1(X0))
| g_false_only(sK1(X0),X0)
| ~ g_true_only(sK1(X0),sK1(X0))
| g_both(X1,X0)
| ~ g_true_only(sK1(X0),X0)
| g_both(X1,X1) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f106,plain,
( ~ spl4_2
| spl4_7 ),
inference(avatar_split_clause,[],[f52,f104,f83]) ).
fof(f108,definition,
( spl4_8
<=> ! [X0,X1] :
( g_both(X1,X0)
| ~ g_both(sK1(X0),sK1(X0))
| g_false_only(sK1(X0),sK1(X0))
| ~ g_both(sK1(X0),X0)
| ~ g_true_only(sK1(X0),X0)
| g_both(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
fof(f109,plain,
( ! [X0,X1] :
( g_false_only(sK1(X0),sK1(X0))
| ~ g_both(sK1(X0),sK1(X0))
| g_both(X1,X0)
| ~ g_both(sK1(X0),X0)
| ~ g_true_only(sK1(X0),X0)
| g_both(X1,X1) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f110,plain,
( ~ spl4_2
| spl4_8 ),
inference(avatar_split_clause,[],[f51,f108,f83]) ).
fof(f111,plain,
~ g_false_only(sK2,sK2),
inference(factoring,[],[f35]) ).
fof(f113,plain,
! [X0,X1] :
( ~ g_false_only(X0,X1)
| g_both(X0,X1) ),
inference(resolution,[],[f70,f46]) ).
fof(f114,plain,
! [X0,X1] :
( g_both(X0,X1)
| g_true_only(X0,X1) ),
inference(resolution,[],[f71,f68]) ).
fof(f124,plain,
! [X0] :
( g_both(X0,X0)
| ~ g_true_only(X0,sK2)
| ~ g_both(X0,sK2) ),
inference(resolution,[],[f74,f62]) ).
fof(f125,plain,
! [X0] :
( ~ g_false_only(X0,X0)
| ~ g_true_only(X0,sK2)
| ~ g_both(X0,sK2) ),
inference(resolution,[],[f74,f35]) ).
fof(f126,plain,
! [X0] :
( ~ g_false_only(X0,sK2)
| ~ g_true_only(X0,X0)
| ~ g_both(X0,X0) ),
inference(resolution,[],[f74,f35]) ).
fof(f129,plain,
( ~ g_both(sK2,sK2)
| ~ g_true_only(sK2,sK2) ),
inference(resolution,[],[f74,f111]) ).
fof(f131,definition,
( spl4_9
<=> g_true_only(sK2,sK2) ),
introduced(definition,[new_symbols(definition,[spl4_9])],[avatar_definition]) ).
fof(f133,plain,
( ~ g_true_only(sK2,sK2)
| spl4_9 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f135,definition,
( spl4_10
<=> g_both(sK2,sK2) ),
introduced(definition,[new_symbols(definition,[spl4_10])],[avatar_definition]) ).
fof(f137,plain,
( ~ g_both(sK2,sK2)
| spl4_10 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f138,plain,
( ~ spl4_9
| ~ spl4_10 ),
inference(avatar_split_clause,[],[f129,f135,f131]) ).
fof(f139,plain,
( g_true_only(sK2,sK2)
| spl4_9 ),
inference(resolution,[],[f133,f59]) ).
fof(f142,plain,
( spl4_9
| spl4_9 ),
inference(avatar_split_clause,[],[f139,f131,f131]) ).
fof(f147,plain,
! [X0] :
( ~ g_both(X0,sK2)
| ~ g_both(X0,X0)
| ~ g_true_only(X0,sK2)
| ~ g_true_only(X0,X0) ),
inference(resolution,[],[f125,f74]) ).
fof(f153,plain,
! [X0] :
( ~ g_both(X0,sK2)
| ~ g_true_only(X0,sK2)
| ~ g_true_only(X0,X0)
| ~ g_true_only(X0,sK2)
| ~ g_both(X0,sK2) ),
inference(resolution,[],[f147,f124]) ).
fof(f156,plain,
! [X0] :
( ~ g_both(X0,sK2)
| ~ g_true_only(X0,sK2)
| ~ g_true_only(X0,X0) ),
inference(duplicate_literal_removal,[],[f153]) ).
fof(f158,plain,
! [X0] :
( ~ g_false_only(X0,X0)
| ~ g_true_only(X0,X0)
| ~ g_true_only(X0,sK2) ),
inference(resolution,[],[f156,f60]) ).
fof(f175,plain,
( ! [X0] :
( g_both(X0,sK2)
| ~ g_both(sK1(sK2),sK2)
| ~ g_true_only(sK1(sK2),sK1(sK2))
| ~ g_both(sK1(sK2),sK1(sK2))
| g_both(X0,X0)
| ~ g_true_only(sK1(sK2),sK1(sK2))
| ~ g_both(sK1(sK2),sK1(sK2)) )
| ~ spl4_6 ),
inference(resolution,[],[f101,f126]) ).
fof(f179,plain,
( ! [X0] :
( g_both(X0,sK2)
| ~ g_both(sK1(sK2),sK2)
| ~ g_true_only(sK1(sK2),sK1(sK2))
| ~ g_both(sK1(sK2),sK1(sK2))
| g_both(X0,X0) )
| ~ spl4_6 ),
inference(duplicate_literal_removal,[],[f175]) ).
fof(f181,definition,
( spl4_11
<=> g_both(sK1(sK2),sK1(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition]) ).
fof(f183,plain,
( ~ g_both(sK1(sK2),sK1(sK2))
| spl4_11 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f185,definition,
( spl4_12
<=> g_true_only(sK1(sK2),sK1(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_12])],[avatar_definition]) ).
fof(f189,definition,
( spl4_13
<=> g_both(sK1(sK2),sK2) ),
introduced(definition,[new_symbols(definition,[spl4_13])],[avatar_definition]) ).
fof(f191,plain,
( ~ g_both(sK1(sK2),sK2)
| spl4_13 ),
inference(avatar_component_clause,[],[f189]) ).
fof(f193,definition,
( spl4_14
<=> ! [X0] :
( g_both(X0,sK2)
| g_both(X0,X0) ) ),
introduced(definition,[new_symbols(definition,[spl4_14])],[avatar_definition]) ).
fof(f194,plain,
( ! [X0] :
( g_both(X0,sK2)
| g_both(X0,X0) )
| ~ spl4_14 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f195,plain,
( ~ spl4_11
| ~ spl4_12
| ~ spl4_13
| spl4_14
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f179,f100,f193,f189,f185,f181]) ).
fof(f196,plain,
( g_true_only(sK1(sK2),sK1(sK2))
| spl4_13 ),
inference(resolution,[],[f191,f61]) ).
fof(f198,plain,
( g_true_only(sK1(sK2),sK2)
| spl4_13 ),
inference(resolution,[],[f191,f114]) ).
fof(f199,plain,
( spl4_12
| spl4_13 ),
inference(avatar_split_clause,[],[f196,f189,f185]) ).
fof(f201,plain,
( ! [X0,X1] :
( g_false_only(sK1(X0),X0)
| ~ g_true_only(sK1(X0),sK1(X0))
| g_both(X1,X0)
| ~ g_true_only(sK1(X0),X0)
| g_both(X1,X1)
| ~ g_true_only(sK1(X0),sK1(X0))
| ~ g_true_only(sK1(X0),sK2) )
| ~ spl4_7 ),
inference(resolution,[],[f105,f158]) ).
fof(f206,plain,
( ! [X0,X1] :
( g_false_only(sK1(X0),X0)
| ~ g_true_only(sK1(X0),sK1(X0))
| g_both(X1,X0)
| ~ g_true_only(sK1(X0),X0)
| g_both(X1,X1)
| ~ g_true_only(sK1(X0),sK2) )
| ~ spl4_7 ),
inference(duplicate_literal_removal,[],[f201]) ).
fof(f208,plain,
( g_true_only(sK1(sK2),sK1(sK2))
| spl4_11 ),
inference(resolution,[],[f183,f114]) ).
fof(f213,definition,
( spl4_15
<=> g_true_only(sK1(sK2),sK2) ),
introduced(definition,[new_symbols(definition,[spl4_15])],[avatar_definition]) ).
fof(f215,plain,
( ~ g_true_only(sK1(sK2),sK2)
| spl4_15 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f217,definition,
( spl4_16
<=> g_false_only(sK1(sK2),sK2) ),
introduced(definition,[new_symbols(definition,[spl4_16])],[avatar_definition]) ).
fof(f218,plain,
( ~ g_false_only(sK1(sK2),sK2)
| spl4_16 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f219,plain,
( g_false_only(sK1(sK2),sK2)
| ~ spl4_16 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f221,plain,
( $false
| spl4_13
| spl4_15 ),
inference(resolution,[],[f215,f198]) ).
fof(f222,plain,
( g_true_only(sK1(sK2),sK1(sK2))
| spl4_15 ),
inference(resolution,[],[f215,f59]) ).
fof(f223,plain,
( g_both(sK1(sK2),sK1(sK2))
| spl4_15 ),
inference(resolution,[],[f215,f58]) ).
fof(f224,plain,
( spl4_13
| spl4_15 ),
inference(avatar_contradiction_clause,[],[f221]) ).
fof(f225,plain,
( spl4_11
| spl4_15 ),
inference(avatar_split_clause,[],[f223,f213,f181]) ).
fof(f226,plain,
( spl4_12
| spl4_15 ),
inference(avatar_split_clause,[],[f222,f213,f185]) ).
fof(f229,plain,
( ~ g_both(sK1(sK2),sK2)
| ~ g_true_only(sK1(sK2),sK2)
| spl4_16 ),
inference(resolution,[],[f218,f74]) ).
fof(f230,plain,
( ~ spl4_15
| ~ spl4_13
| spl4_16 ),
inference(avatar_split_clause,[],[f229,f217,f189,f213]) ).
fof(f251,plain,
( ! [X0,X1] :
( g_both(sK1(X0),X0)
| g_both(X1,X0)
| ~ g_true_only(sK1(X0),X0)
| g_both(X1,X1)
| ~ g_true_only(sK1(X0),sK2)
| ~ g_true_only(sK1(X0),sK1(X0)) )
| ~ spl4_7 ),
inference(resolution,[],[f206,f113]) ).
fof(f256,plain,
( ! [X0] :
( g_both(X0,sK2)
| ~ g_true_only(sK1(sK2),sK2)
| g_both(X0,X0)
| ~ g_true_only(sK1(sK2),sK2)
| ~ g_true_only(sK1(sK2),sK1(sK2))
| ~ g_true_only(sK1(sK2),sK2)
| ~ g_true_only(sK1(sK2),sK1(sK2)) )
| ~ spl4_7 ),
inference(resolution,[],[f251,f156]) ).
fof(f257,plain,
( ! [X0] :
( g_both(X0,sK2)
| ~ g_true_only(sK1(sK2),sK2)
| g_both(X0,X0)
| ~ g_true_only(sK1(sK2),sK1(sK2)) )
| ~ spl4_7 ),
inference(duplicate_literal_removal,[],[f256]) ).
fof(f261,plain,
( ! [X0,X1] :
( ~ g_false_only(sK1(X0),sK2)
| g_both(X1,X0)
| ~ g_both(sK1(X0),X0)
| ~ g_true_only(sK1(X0),X0)
| g_both(X1,X1)
| ~ g_both(sK1(X0),sK1(X0)) )
| ~ spl4_8 ),
inference(resolution,[],[f109,f35]) ).
fof(f268,plain,
( ! [X0] :
( g_both(X0,sK2)
| ~ g_both(sK1(sK2),sK2)
| ~ g_true_only(sK1(sK2),sK2)
| g_both(X0,X0)
| ~ g_both(sK1(sK2),sK1(sK2)) )
| ~ spl4_8
| ~ spl4_16 ),
inference(resolution,[],[f261,f219]) ).
fof(f273,plain,
( ~ spl4_11
| ~ spl4_15
| ~ spl4_13
| spl4_14
| ~ spl4_8
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f268,f217,f108,f193,f189,f213,f181]) ).
fof(f274,plain,
( spl4_12
| spl4_11 ),
inference(avatar_split_clause,[],[f208,f181,f185]) ).
fof(f301,plain,
( ~ g_true_only(sK2,sK2)
| ~ spl4_1 ),
inference(resolution,[],[f81,f111]) ).
fof(f307,plain,
( ~ spl4_9
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f301,f80,f131]) ).
fof(f310,plain,
( ~ spl4_12
| ~ spl4_15
| spl4_14
| ~ spl4_7 ),
inference(avatar_split_clause,[],[f257,f104,f193,f213,f185]) ).
fof(f382,plain,
( g_both(sK2,sK2)
| spl4_10
| ~ spl4_14 ),
inference(resolution,[],[f194,f137]) ).
fof(f386,plain,
( spl4_10
| spl4_10
| ~ spl4_14 ),
inference(avatar_split_clause,[],[f382,f193,f135,f135]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f86]) ).
cnf(s5,plain,
( ~ spl4_2
| spl4_6 ),
inference(sat_conversion,[],[f102]) ).
cnf(s6,plain,
( ~ spl4_2
| spl4_7 ),
inference(sat_conversion,[],[f106]) ).
cnf(s7,plain,
( ~ spl4_2
| spl4_8 ),
inference(sat_conversion,[],[f110]) ).
cnf(s8,plain,
( ~ spl4_9
| ~ spl4_10 ),
inference(sat_conversion,[],[f138]) ).
cnf(s10,plain,
( spl4_9
| spl4_9 ),
inference(sat_conversion,[],[f142]) ).
cnf(s11,plain,
spl4_9,
inference(rat,[],[s10]) ).
cnf(s12,plain,
( ~ spl4_6
| ~ spl4_11
| ~ spl4_12
| ~ spl4_13
| spl4_14 ),
inference(sat_conversion,[],[f195]) ).
cnf(s13,plain,
( spl4_12
| spl4_13 ),
inference(sat_conversion,[],[f199]) ).
cnf(s15,plain,
( spl4_13
| spl4_15 ),
inference(sat_conversion,[],[f224]) ).
cnf(s16,plain,
( spl4_11
| spl4_15 ),
inference(sat_conversion,[],[f225]) ).
cnf(s17,plain,
( spl4_12
| spl4_15 ),
inference(sat_conversion,[],[f226]) ).
cnf(s18,plain,
( ~ spl4_13
| ~ spl4_15
| spl4_16 ),
inference(sat_conversion,[],[f230]) ).
cnf(s19,plain,
( ~ spl4_8
| ~ spl4_11
| ~ spl4_13
| spl4_14
| ~ spl4_15
| ~ spl4_16 ),
inference(sat_conversion,[],[f273]) ).
cnf(s20,plain,
( spl4_11
| spl4_12 ),
inference(sat_conversion,[],[f274]) ).
cnf(s30,plain,
( ~ spl4_1
| ~ spl4_9 ),
inference(sat_conversion,[],[f307]) ).
cnf(s32,plain,
( ~ spl4_7
| ~ spl4_12
| spl4_14
| ~ spl4_15 ),
inference(sat_conversion,[],[f310]) ).
cnf(s46,plain,
( spl4_10
| spl4_10
| ~ spl4_14 ),
inference(sat_conversion,[],[f386]) ).
cnf(s47,plain,
( spl4_10
| ~ spl4_14 ),
inference(rat,[],[s46]) ).
cnf(s49,plain,
~ spl4_1,
inference(rat,[],[s30,s11]) ).
cnf(s50,plain,
~ spl4_10,
inference(rat,[],[s8,s11]) ).
cnf(s51,plain,
~ spl4_14,
inference(rat,[],[s47,s50]) ).
cnf(s52,plain,
spl4_2,
inference(rat,[],[s1,s49]) ).
cnf(s53,plain,
spl4_8,
inference(rat,[],[s7,s52]) ).
cnf(s54,plain,
spl4_7,
inference(rat,[],[s6,s52]) ).
cnf(s55,plain,
spl4_6,
inference(rat,[],[s5,s52]) ).
cnf(s56,plain,
spl4_11,
inference(rat,[],[s32,s16,s20,s51,s54]) ).
cnf(s57,plain,
~ spl4_12,
inference(rat,[],[s15,s12,s32,s55,s56,s51,s54]) ).
cnf(s58,plain,
spl4_15,
inference(rat,[],[s17,s57]) ).
cnf(s59,plain,
spl4_13,
inference(rat,[],[s13,s57]) ).
cnf(s60,plain,
spl4_16,
inference(rat,[],[s18,s58,s59]) ).
cnf(s61,plain,
$false,
inference(rat,[],[s19,s58,s56,s51,s53,s60,s59]) ).
fof(f388,plain,
$false,
inference(avatar_sat_refutation,[],[s61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV515+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.17/0.43 % Computer : n008.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 28 06:30:54 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.21/0.48 Running first-order model finding
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.51 % (2043775)Will run a generic schedule for satisfiability detection.
% 0.21/0.51 % (2043786)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=566952699:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.21/0.51 % (2043786) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2043775-2043786"...
% 0.21/0.51 % (2043781)% WARNING: option uhcvi not known.
% 0.21/0.51 % (2043786)...printing done.
% 0.21/0.51 % (2043786)Refutation found. Thanks to Tanya!
% 0.21/0.51 % SZS status Theorem for theBenchmark
% 0.21/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.52 % (2043786)------------------------------
% 0.21/0.52 % (2043786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.52 % (2043786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.52 % (2043786)CaDiCaL version: 2.1.3
% 0.21/0.52 % (2043786)Termination reason: Refutation
% 0.21/0.52 % (2043786)Time elapsed: 0.007 s
% 0.21/0.52 % (2043786)Peak memory usage: 12 MB
% 0.21/0.52 % (2043786)Instructions burned: 10 (million)
% 0.21/0.52 % (2043775)Success in time 0.03 s
% 0.21/0.52 % Vampire exiting
%------------------------------------------------------------------------------